### A Hybrid Simulated Annealing And Gradient-Based Algorithm For The Estimation Of Unsaturated Soil Parameters

#### Abstract

Simulation of water flow in the unsaturated zone requires knowledge of hydraulic conductivity

and water content functions. In most applied studies these functions are described by the well-known

van Genuchten constitutive model, which has five independent parameters. Model parameters are usually

determined from laboratory experiments, although often these estimates are non-representative of field

conditions. In recent years, the use of inverse methods in conjunction with field experiments has become

a promising alternative for the accurate estimation of unsaturated soil parameters. Essentially, this procedure

involves the minimization of a cost or objective function that measures the discrepancy between

observed and simulated data. In the present work we estimate the van Genuchten model parameters from

hypothetical drainage experiments using a hybrid optimization strategy based on simulated annealing

and a quasi-Newton method. Drainage experiments are modeled by solving Richards equation with appropriate

initial and boundary conditions. To obtain approximate solutions of Richards equation we use

a Galerkin finite element method. The algorithm behavior and the consequences on the estimated van

Genuchten model parameters using different objective functions are explored. Objective functions are

constructed from two sets of data which are usually obtained on field experiments: pressure head p versus

time measured at different depths and water content versus depth measured at different times. The

proposed estimation procedure is tested using synthetically generated data. Numerical examples show

that the inverse modeling of drainage experiments using a hybrid simulated annealing and gradient-based

algorithm provides an excellent methodology for an efficient and accurate estimation of unsaturated soil

parameters.

and water content functions. In most applied studies these functions are described by the well-known

van Genuchten constitutive model, which has five independent parameters. Model parameters are usually

determined from laboratory experiments, although often these estimates are non-representative of field

conditions. In recent years, the use of inverse methods in conjunction with field experiments has become

a promising alternative for the accurate estimation of unsaturated soil parameters. Essentially, this procedure

involves the minimization of a cost or objective function that measures the discrepancy between

observed and simulated data. In the present work we estimate the van Genuchten model parameters from

hypothetical drainage experiments using a hybrid optimization strategy based on simulated annealing

and a quasi-Newton method. Drainage experiments are modeled by solving Richards equation with appropriate

initial and boundary conditions. To obtain approximate solutions of Richards equation we use

a Galerkin finite element method. The algorithm behavior and the consequences on the estimated van

Genuchten model parameters using different objective functions are explored. Objective functions are

constructed from two sets of data which are usually obtained on field experiments: pressure head p versus

time measured at different depths and water content versus depth measured at different times. The

proposed estimation procedure is tested using synthetically generated data. Numerical examples show

that the inverse modeling of drainage experiments using a hybrid simulated annealing and gradient-based

algorithm provides an excellent methodology for an efficient and accurate estimation of unsaturated soil

parameters.

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**